Sorry for the late reply; these issues are complicated and take a lot of thinking. And though I don’t claim to have presented rock-solid unassailable arguments here, I can still try, rather than simply say that the questions are unanswerable.
As Block says, apply the rule of homesteading (i.e., first come first served). If I’m driving on a busy highway, and suddenly I’m struck blind, I no longer have the right to keep driving and crash - the other drivers “homesteaded” their rights to life from before my blindness. So with your examples, it’s ethical to quarantine the person who is a newly-become threat to others. Note, however, that the opposite is true if it’s the other way around: if I suddenly change such that carbon dioxide is deadly to me, I don’t have the right to stop everyone else from breathing - I have the first claim to the misery that nature has sent me.
Practically speaking, for one, it’s exceedingly unlikely that 99% of the population would suddenly become dangerous - it’s much more likely that 1% would become vulnerable. Also, if human immune systems are so ill-prepared that a naturally-evolved virus has the potential to kill 5 billion people, then I’d say you’re pretty much screwed no matter what you do.
This scenario is very non-specific, so I’ll have to add a lot of qualifiers.
First of all, we would have to know the extent to which the Spaniards were causally responsible for the epidemics. For example, suppose that after a 3-week drought in a fire-prone area, there is a forest fire that causes millions of dollars’ worth of damage. Suppose then it’s discovered that the fire was started by someone who carelessly threw a cigarette off the side of the road. Is this person liable for all the damage? I would say, no, because forest fires are a part of nature, and at most the cigarette-thrower could be held liable for the fact that the fire occurred slightly earlier than it otherwise would have. However, assuming that the pathogenic ecosystem of the Americas was long-term stable, then yes, the natives have a good enough reason to compel the Spaniards to leave (or quarantine themselves, etc.). On the other hand, if neither the natives nor the Spaniards at all knew that the Spaniards were spreading viruses (which would be a little hard not to notice, granted), and the Spaniards have not been negligent in gathering this information (again a big if), then I think there is no basis for a liability claim by the natives against the Spaniards, even if the viruses are discovered in retrospect. In any case, killing the Spaniards is excessive, since whatever this could accomplish could also be accomplished by making them leave (assuming that the virus hasn’t spread yet). I have assumed throughout that the Spaniards were not trespassing on the natives’ property, which makes it easy to decide who’s right.
What would qualify as a “universal” answer? Do you think that arguing about these cases is completely superfluous? After all, even an arbitrator needs some basis on which to make a decision. If parties have brought a conflict to an arbitrator, then they already believe that there is some answer to their dispute, or else they would have just agreed to disagree. And since both parties are agreed on this point, the arbitrator may assume as much when making a decision.